They’re currently six points behind their rivals and two ahead of Real Madrid.
Messi has played a key role in their recent rise and the Barcelona star seems far happier on the pitch than he did earlier in the campaign.
Joan Laporta, who has a good relationship with the Argentina international, has replaced Josep Maria Bartomeu as Barcelona president.
And PSG fear that close connection could now see them miss out.
They’re also concerned about the futures of Kylian Mbappe and Neymar, with the Ligue 1 giants yet to tie them down to a new contracts.